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All the acrimony in the primary race between Barack Obama and Hillary Clinton has disguised the fact that on most issues they’re not too far apart. That’s especially the case when it comes to free trade, which both Obama and Clinton have lambasted over the past few months.

At times, the campaign has looked like a contest over who hates free trade more: Obama has argued that free-trade agreements like NAFTA are bought and paid for by special interests, while Clinton has emphasized the need to “stand up” to countries like China. Two weeks ago, both senators signed on as sponsors of a new bill that would effectively impose higher tariffs on China if it doesn’t revalue its currency.

The candidates are trying to win the favor of unions and blue-collar voters in states like Ohio and West Virginia, of course, but their positions also reflect a widespread belief that free trade with developing countries, and with China in particular, is a kind of scam perpetrated by the wealthy, who reap the benefits while ordinary Americans bear the cost.

It’s an understandable view: how, after all, can it be a good thing for American workers to have to compete with people who get paid seventy cents an hour? As it happens, the negative effect of trade on American wages isn’t that easy to document. The economist Paul Krugman, for instance, believes that the effect is significant, though in a recent academic paper he concluded that it was impossible to quantify.

But it’s safe to say that the main burden of trade-related job losses and wage declines has fallen on middle- and lower-income Americans. So standing up to China seems like a logical way to help ordinary Americans do better. But there’s a problem with this approach: the very people who suffer most from free trade are often, paradoxically, among its biggest beneficiaries.

The reason for this is simple: free trade with poorer countries has a huge positive impact on the buying power of middle- and lower-income consumers — a much bigger impact than it does on the buying power of wealthier consumers. The less you make, the bigger the percentage of your spending that goes to manufactured goods — clothes, shoes, and the like — whose prices are often directly affected by free trade. The wealthier you are, the more you tend to spend on services — education, leisure, and so on — that are less subject to competition from abroad.

In a recent paper on the effect of trade with China, the University of Chicago economists Christian Broda and John Romalis estimate that poor Americans devote around forty percent more of their spending to “non-durable goods” than rich Americans do. That means that lower-income Americans get a much bigger benefit from the lower prices that trade with China has brought.

Then, too, the specific products that middle- and lower-income Americans buy are much more likely to originate in places like China than the products that wealthier Americans buy. Despite a huge increase in imports from China — they sextupled as a percentage of U.S. imports between 1990 and 2006 — Chinese products are still concentrated mostly in lower-price markets. (By some estimates, Wal-Mart alone has accounted for nearly a tenth of all imports from China in recent years.)

By contrast, much of what wealthier Americans buy is made in the U.S. or in high-wage countries like Germany and Switzerland. This is obvious when it comes to luxury goods — Louis Vuitton bags, Patek Philippe watches, and so on — but it’s also true of many other goods, like electronics, kitchen appliances, and furniture, categories in which American and European manufacturers have continued to thrive by selling to the high-end market. According to the Yale economist Peter K. Schott, machinery and electronics products made in developed countries sell in the U.S. for four times the average price of Chinese products. And, since the late 1980s, that price gap has widened by almost 40 percent.

This may not always be the case; as China’s economy continues to boom, its companies will likely move up the quality ladder and, eventually, become serious competition for high-end American and European manufacturers. But for the moment the benefits of free trade with China, at least when it comes to shopping, are concentrated overwhelmingly among average Americans. And the result is that, in the past decade, the products that they spend more on have become a lot cheaper compared to the stuff that rich people spend more on.

Broda and Romalis, in their recent paper, calculate that between 1999 and 2005 alone the inflation rate for lower-income Americans was almost seven points lower than it was for the wealthiest Americans. That means that free trade with China has made average Americans, at least as consumers, much better off—in the sense that it’s made their dollars go further than they otherwise would have.

Now, there’s a lot that’s left out of this equation, such as the fact that free trade may help richer Americans by increasing corporate profits. And cheap DVD players may not, on balance, make up for lost jobs. But the reality is that if we toughen our trade relations with China the benefits will be enjoyed by a few, since only a small percentage of Americans now work for companies that compete directly with Chinese manufacturers, while average Americans will feel the pain—in the form of higher prices—far more quickly and more directly than rich Americans will.

Obama and Clinton, in their desire to help working Americans—and gain their votes—are pushing for policies that will also hurt them.